You can absolutely, and very easily, include your own files in a custom image, you don't even need to do a full custom build for that, the "abbreviated" image builder will do that just fine. But I actually never tried removing single files, according to the documentation it should be possible but it's a bit of a hassle since it's not something the image builder does out of the box.
I don't quite understand what you mean. If you manually, after installing, added a file to the system you can just remove it again. Just like you cannot remove files from the squashfs file system, you also cannot add files to it. Files you install afterwards are not kept in squashfs, but in the overlayfs file system (that, as the name implies, sits "on top" of the squashfs file system and keeps the modifications.)